Mensuration Worksheet for Maths Olympiad

Maths Olympiad topic 26: Mensuration: circles, surface area and volume · Set 265 · 40 questions

How to solve it (Divide by 7 first): Circle: circumference = 2 × π × r; area = π × r × r. With π = 22/7, divide the radius by 7 first. Cube of edge a: volume = a × a × a, surface area = 6 × a × a. Cuboid: volume = l × b × h, surface area = 2 × (lb + bh + hl). Make every length k times as long: areas become k × k times as big, volumes k × k × k times.

1. 1.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 132 sq cm (d) 1386 sq cm
2. 2.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
4. 4.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
5. 5.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
6. 6.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
7. 7.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
9. 9.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 9856 sq cm
10. 10.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 4 times (c) 8 times (d) 2 times
11. 11.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
12. 12.A cube has edges of 12 cm. What is its volume? (a) 1728 cu cm (b) 36 cu cm (c) 576 cu cm (d) 864 cu cm
13. 13.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 4 times (c) 8 times (d) 2 times
15. 15.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
16. 16.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 88 sq cm
17. 17.A cuboid is 9 cm long, 4 cm wide and 4 cm high. What is its volume? (a) 176 cu cm (b) 144 cu cm (c) 17 cu cm (d) 36 cu cm
18. 18.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 6 times (c) 27 times (d) 3 times
19. 19.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 384 sq cm (d) 256 sq cm
20. 20.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
21. 21.A cuboid is 9 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 230 cu cm (b) 19 cu cm (c) 225 cu cm (d) 45 cu cm
22. 22.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 5 times (c) 25 times (d) 125 times
23. 23.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
24. 24.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
25. 25.A cuboid is 8 cm long, 2 cm wide and 9 cm high. What is its total surface area? (a) 424 sq cm (b) 144 sq cm (c) 212 sq cm (d) 106 sq cm
26. 26.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 22 cm (d) 44 cm
27. 27.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 100 cu cm (c) 15 cu cm (d) 150 cu cm
28. 28.A cuboid is 10 cm long, 8 cm wide and 7 cm high. What is its volume? (a) 560 cu cm (b) 25 cu cm (c) 412 cu cm (d) 80 cu cm
29. 29.A cuboid is 4 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 56 sq cm (b) 224 sq cm (c) 112 sq cm (d) 64 sq cm
30. 30.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 96 sq cm (d) 16 sq cm
31. 31.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 30 cu cm (c) 1000 cu cm (d) 400 cu cm
32. 32.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
33. 33.A cuboid is 7 cm long, 6 cm wide and 3 cm high. What is its total surface area? (a) 126 sq cm (b) 324 sq cm (c) 162 sq cm (d) 81 sq cm
34. 34.A cube has edges of 7 cm. What is its volume? (a) 343 cu cm (b) 196 cu cm (c) 294 cu cm (d) 21 cu cm
35. 35.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 12 cu cm (c) 96 cu cm (d) 64 cu cm
36. 36.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 15 cu cm (d) 136 cu cm
37. 37.A cuboid is 4 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 50 sq cm (b) 56 sq cm (c) 100 sq cm (d) 200 sq cm
38. 38.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
39. 39.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 72 sq cm (b) 144 sq cm (c) 36 sq cm (d) 73 sq cm
40. 40.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 110 cm (d) 3850 cm

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